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In this article, we consider the following fractional (p , q) -Laplacian problem (− Δ) p s 1 u + (− Δ) q s 2 u + V (x) (| u | p − 2 u + | u | q − 2 u) = f (u) + λ | u | r − 2 u , where x ∈ R N , (− Δ) p s 1 is the fractional p-Laplacian operator ( (− Δ) q s 2 is similar), 0 < s 1 < s 2 < 1 < p < q < N s 2 , q s 2 * = N q N − s 2 q , r ≥ q s 2 * , f is a C 1 real function and V is a coercive function. By using variational methods, we prove that the above problem admits a sign-changing solution if λ > 0 is small. [ABSTRACT FROM AUTHOR]

This paper gives some results on almost automorphic strong solutions to time-fractional partial differential equations by employing a mix o thef Galerkin method, Fourier series, and Picard iteration. As an application, the existence, uniqueness, and global Mittag–Leffler convergence of almost automorphic strong solution are discussed to a concrete time-fractional parabolic equations. To the best of our knowledge, this is the first study on almost automorphic strong solutions on this subject. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonlinear impulsive generalized fractional differential equations with (p , q) -Laplacian operator for 1 < p ≤ q < ∞ , in which the nonlinearity f contains two fractional derivatives with respect to another function. Since the complexity of the nonlinear term and the impulses exist in generalized fractional calculus, it is difficult to find the corresponding variational functional of the problem. The existence of nontrivial solutions for the problem is established by the mountain pass theorem and iterative technique under some appropriate assumptions. Furthermore, our main result is demonstrated by an illustrative example to show its feasibility and effectiveness. Due to the employment of a generalized fractional operator, our results extend some existing research findings. [ABSTRACT FROM AUTHOR]